Solve 7/8div(-7/9--11/8)

$$\frac { 7 } { 8 } \div ( \frac { - 7 } { 9 } - \frac { - 11 } { 8 } )$$

Evaluate

$$\frac{63}{43}\approx 1.465116279$$

Solution Steps

Fraction \frac{-7}{9} can be rewritten as -\frac{7}{9} by extracting the negative sign.

$$\frac{\frac{7}{8}}{-\frac{7}{9}-\frac{-11}{8}}$$

Fraction \frac{-11}{8} can be rewritten as -\frac{11}{8} by extracting the negative sign.

$$\frac{\frac{7}{8}}{-\frac{7}{9}-\left(-\frac{11}{8}\right)}$$

The opposite of -\frac{11}{8} is \frac{11}{8}.

$$\frac{\frac{7}{8}}{-\frac{7}{9}+\frac{11}{8}}$$

Least common multiple of 9 and 8 is 72. Convert -\frac{7}{9} and \frac{11}{8} to fractions with denominator 72.

$$\frac{\frac{7}{8}}{-\frac{56}{72}+\frac{99}{72}}$$

Since -\frac{56}{72} and \frac{99}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{8}}{\frac{-56+99}{72}}$$

Add -56 and 99 to get 43.

$$\frac{\frac{7}{8}}{\frac{43}{72}}$$

Divide \frac{7}{8} by \frac{43}{72} by multiplying \frac{7}{8} by the reciprocal of \frac{43}{72}.

$$\frac{7}{8}\times \frac{72}{43}$$

Multiply \frac{7}{8} times \frac{72}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 72}{8\times 43}$$

Do the multiplications in the fraction \frac{7\times 72}{8\times 43}.

$$\frac{504}{344}$$

Reduce the fraction \frac{504}{344} to lowest terms by extracting and canceling out 8.

$$\frac{63}{43}$$

Factor

$$\frac{3 ^ {2} \cdot 7}{43} = 1\frac{20}{43} = 1.4651162790697674$$